This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

Recent works in evolutionary multiobjective optimization suggest to shift the focus from solely evaluating optimization success in the objective space to also taking the decision space into account. They indicate that this may be a) necessary to express the users requirements of obtaining distinct solutions (distinct Pareto set parts or subsets) of similar quality (comparable locations on the P...

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill...

We describe techniques for visualizing the Pareto optimal set that can be used if the multiobjective optimization problem considered has more than two objective functions. The techniques discussed can be applied in the framework of both MCDM and EMO approaches. First, lessons learned from methods developed for biobjective problems are considered. Then, visualization techniques for convex multio...

The optimal design of a plate-fin recuperator of a 200-kW microturbine was studied in this paper. The exergy efficiency, pressure drop and total cost were selected as the three important objective functions of the recuperator. Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm (NSGA-II) were respectively employed for single-objective and multi-objective optimizations. By opt...

In the field of multiobjective optimization, important efforts have been made in recent years to generate global Pareto fronts uniformly distributed. A new multiobjective evolutionary algorithm, called ↗−MOGA, has been designed to converge towards ΘP , a reduced but well distributed representation of the Pareto set ΘP . The algorithm achieves good convergence and distribution of the Pareto fron...

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as Multi-objective Optimization Problems (MOPs)) has attracted much attention recently. Being population based approaches, EAs offer a means to find a group of pareto-optimal solutions in a single run. Differential Evolution (DE) is an EA that was developed to handle optimization problems over continuous ...

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

The use of evolutionary strategies (ESs) to solve problems with multiple objectives (known as Vector Optimization Problems (VOPs)) has attracted much attention recently. Being population based approaches, ESs offer a means to find a set of Pareto-optimal solutions in a single run. Differential Evolution (DE) is an ES that was developed to handle optimization problems over continuous domains. Th...